Anchor deformations drive limit cycle oscillations in interferometrically transduced MEMS beams

A micro-scale resonator suspended over a substrate and illuminated with a continuous wave (CW) laser forms an interferometer which couples deflection of the resonator to light absorption. In turn, absorption creates temperature and thermal stress fields which feedback into the motion. Experiments have shown that this coupling can lead to limit cycle oscillations in which the resonator vibrates in the absence of external forcing. However, the mechanism by which the thermal stresses drive limit cycle oscillations of initially flat beams was unknown. In this paper, we present a thermo-mechanical finite element method (FEM) analysis of doubly clamped beams which shows that the combination of anchor point thermal gradients and deflection due to compression couples out-of-plane motion of the beam to the thermal field. It is this coupling that makes limit cycle oscillations of the beam resonators possible. Results of the FEM analysis are used to compute the threshold laser power needed for limit cycle oscillations.